Fig. 1: Illustration of the generation of density fingerprint.
From: Geometric data analysis-based machine learning for two-dimensional perovskite design
In this example, the unit cell U is the set \({\left[0,1\right)}^{3}\) with the atoms centered at the vertices, and S(t) are atom spheres with radius t. Panel a: The overlapping region of k spheres (within the unit cell) is denoted as U ∩ ⋃kS(t) (k = 0, 1, 2, 3); Panel b: The overlapping region of exactly k spheres (within the unit cell) is \(U\cap ({\bigcup }^{k}S(t)-{\bigcup }^{k+1}S(t))\) (k = 0, 1, 2); Panel c: The corresponding density functions ψ0, ψ1, ψ2 on the interval [0, 1].
